Walters researchers decode the secrets of the Archimedes Palimpsest

Findings shed new light on the accomplishments of the famed Greek mathematician

By Mary Carole McCauley, The Baltimore Sun

7:02 PM EDT, October 14, 2011


Twelve years ago, Walters Art Museum curator Will Noel opened a parcel and discovered what he calls "Archimedes' brain in a box."

Thus began a search for buried treasure — in this case, the lost writings of Archimedes of Syracuse, a famed Greek mathematician and inventor who lived in the third century B.C.

Noel and his boss, museum director Gary Vikan, found a 174-page book made of cured goatskin that was ugly beyond belief. The sheaves were singed around the edges, the text and pages were defaced by water stains, and mold had eaten away entire sections.

Noel began to gently riffle through the pages but stopped when they fell apart in his hands. "It looked as though it had been in a fire, or something had chewed it up," Vikan says. "It made me think of shredded wheat."

Even worse, the manuscript had been washed and scraped away by a medieval monk and written over with prayers (making it a "palimpsest," a document in which the original text has been imperfectly erased and written over.) Only ghostly traces of the original remained.

So Walters assembled two dozen experts worldwide who began to make the nearly invisible visible, aided by technologies being invented as they worked. What they found has changed scholarly understanding not just of ancient mathematics, but also of politics and philosophy in the classical world.

"Lost & Found: The Secrets of Archimedes" opens Sunday at the Walters and runs the rest of the year. The exhibit presents a fascinating modern detective story, as well as a history of the palimpsest populated by heroes and rogues.

"This has been an irrationally exuberant process," says Noel, the Walters' curator of manuscripts and rare books.

"Think of it as a race for survival. On the one hand, Archimedes and the scribes who copied his work are writing as fast as they can. On the other hand, you have the bad guys — war, pestilence, famine, bacteria and neglect.

"Ninety-percent of the time, the bad guys win and the manuscript is lost. We'll never know what's inside. But every now and then, the good guys cross the finish line first."

Archimedes has acquired a pleasantly dotty image over the centuries as the guy who (perhaps apocryphally) leaped from his bathtub after solving a particularly vexing challenge and ran naked through the streets of Syracuse shouting "Eureka!"

Archimedes' legacy extends to mathematical fields as diverse as calculus and computer science. He made groundbreaking discoveries in hydrostatics, which measures the pressure exerted by liquids because of gravity. He invented the catapult, the battering ram, pulleys and siege machines. He was the first person to explain mathematically how levers work. The Archimedes Screw, a mechanical device for raising water, is still used in Third World nations.

But, it wasn't until the scholars visiting the Walters began to decipher the palimpsest that they established Archimedes as the founder of combinatorics, a type of mathematics frequently used in computer coding and game theory.

"The rewriting of history," Noel says, "is a fabulously wonderful and romantic thing."

'Uniquely ugly'

How the palimpsest arrived at the Walters is an improbable story in itself. The small book was auctioned off by Christie's Inc. in 1998 for $2 million, purchased anonymously by a private bidder.

"To you or me, $2 million is a lot of money," Noel says. "But it's cheap for an original manuscript by one of the greatest mathematical minds who ever lived."

But the day before the palimpsest was to be sold, a lawsuit was filed attempting to block the auction, claiming that the manuscript had been stolen from a Jerusalem monastery in the 1920s. Though a federal judge eventually ruled in Christie's favor, not only were other bidders scared off by the scandal, they didn't even try to borrow the palimpsest and decode it.

But Vikan was undeterred.

"Gary is fearless," Noel says.

In a way, the Walters is an unlikely home for the book, even temporarily. The Walters is a midsize art museum, and Archimedes was a mathematician. The other manuscripts in the Walters' collection are frequently decorated with gold, silver and precious jewels and are strikingly beautiful.

The palimpsest, Noel says, "is uniquely ugly."

But, on Oct. 27, 1998, the day the story about the lawsuit made the front page of The New York Times, Vikan ran into Noel on the Walters' front steps.

"We should try to get that book," Vikan said.

Noel went back to his desk and wrote a long memo explaining why borrowing the palimpsest was a bad idea, but Vikan wasn't swayed.

"I spent the next 12 years," Noel says, "trying not to mess up the opportunity of a lifetime."

Abigail Quandt is the Walters' senior conservator of manuscripts and rare books. It was her job to stabilize the manuscript and prepare the leaves to be photographed.

Because the palimpsest had been used as a prayer book since the Middle Ages, the pages were covered with centuries-old drippings from wax candles. Quandt had to analyze the chemical composition of the parchment and determine if it would stand up to testing. It took nearly four years just to separate the pages from the binding.

"You can't be nervous when you try out new techniques," she says.

"You have to just go with your gut. If there's something sacrificial, if I could find a scrap piece of parchment, I would test it there first. Part of the difficulty was that there was a huge time pressure. But I refused to rush, because if I rushed, there would be mistakes. No one could afford that."

Heroes and villains

The more Quandt and Noel delved into the condition of the palimpsest, the more they learned about the forces — and people — that had altered the book.

The researchers paid their respects to the 10th-century scribe who copied down works by Archimedes of lasting importance. The palimpsest contains the only version of "On Floating Islands" in Greek — the mathematician's native tongue. And it contains the only original versions anywhere of his "Method of Mechanical Theorems" and "The Stomachion."

Surprisingly, Noel sympathizes with Johannes Myrones, the monk who found himself distressingly short of new parchment on April 13, 1229, after Constantinople was sacked by crusaders. It was Myrones who scraped away Archimedes' original writing and converted the used parchment into a religious text.

"If the palimpsest hadn't been converted into a prayer book, it wouldn't have survived for more than 700 years," Noel says. "It survived because it was used."

Then there was the notorious 19th-century scholar and thief Constantin von Tischendorf, who visited the monastery near Jerusalem where the prayer book was kept in the early 1840s. Mysteriously, one leaf was sold to Cambridge University in 1879 by von Tischendorf's estate.

As Noel put it: "He got around."

But the palimpsest also had its saviors.

During a few weeks of his summer vacation in 1906, Archimedes expert Johan Heiberg visited a monastery a few miles west of Bethlehem. It was Heiberg who identified the prayer book as containing Archimedes' mathematical writings, he who translated an impressive chunk of the text using only his unaided eyes, and he who determined that the palimpsest contained previously unknown works.

In fact, Heiberg was such a genius that many people thought he had extracted every bit of useful information that the document contained.

But the Walters researchers wanted to be certain.

So the museum recruited teams of scientists from the Johns Hopkins University and New York's Rochester Institute of Technology, who used imaging technologies first developed for medical and space research.

"New technologies have the potential to fundamentally change how we know things," Noel says. "When we started out, we were delivering images through FedEx."

The scientists bombarded the parchment with light from various spectrums. Some rays were longer than a football field. Others were shorter than an atom. Then the different images were superimposed on top of one another.

"There are things that can be seen in one kind of light that can't be seen in another," Noel says.

They also attacked the problem another way, by placing each sheet in a magnetic field. The ink contained traces of iron that caused detectable changes in the field. The result from all the imaging tests created a kind of topography of the hidden writings. All the major features of the landscape were visible, but they couldn't be viewed up close.

Finally, more detailed results were achieved after the scientists flooded the text with a type of X-ray that created maps of the chemical elements present on individual pages.

At a resolution of 800 dots per inch "the images are just barely good enough for scholars to read," Noel says. "They're rather miraculous."

And what the scholars found amazed them, starting with the geometrical drawings on several pages.

"Heiberg paid no attention to diagrams," Noel says. "He was a lover of language. But ancient mathematicians thought in diagrams. They are part of Archimedes' logic."

In addition, a careful perusal of "The Method" reveals that the ancient Greeks had a far more sophisticated understanding of infinity — perhaps the most crucial concept in all of mathematics — than had been previously suspected.

Another breakthrough was made by Revel Netz, a philosophy professor at Stanford University. He hypothesized a link between "The Stomachion" (in which Archimedes was working on what appeared to be a children's game) to the modern field of cominatorics, which seeks how to determine how many different ways a single problem can be solved. It took modern scholars six weeks to determine that the answer that Archimedes gave for his puzzle — 17,152 — is in fact, correct.

For the researchers, spending 12 years in Archimedes' mind was like inhabiting a dwelling that was spacious, calm and radiated light.

"He's like Bach," Noel says. "His cleverness is beautiful. Understanding Archimedes is like understanding the most elegant joke in the world."

Lost speeches

Finally, the palimpsest also contains works by other authors — most notably, two lost speeches by the famed orator Hyperides.

In 334 B.C., Hyperides was in trouble. Four years earlier, he had advised the generals leading an alliance of Greek city-states to resist an attack by the Macedonians. It turned out to be poor advice. The Athenians were massacred, and Hyperides was prosecuted for treason.

The palimpsest contains the eloquent defense he gave during the trial.

The court, however, was unpersuaded. In 322 B.C., Hyperides' golden tongue was cut out and he was put to death.

Twenty-three centuries later, his voice is being heard again.

"Hyperides was saved by Archimedes," Noel says.

"If his speech wasn't bound up with a text by Archimedes, this project would never have attracted all the scientists who donated their time. We'd never have gone looking for him. He'd still be lost to us today."

After "Lost and Found" closes on Jan. 1, the palimpsest will be returned to its owner. But the scholarship will go on. The 174 sheaves have all been digitally imaged, and they are available online to anyone who wants to look at them.

One day, someone may identify the authors of two other texts contained in the palimpsest.

And that possibility of future discoveries may be the most important legacy of the 12-year-long project.

As Noel puts it: "We've taken something expensive, fragile, inaccessible and unknown and made it available for free to anyone from their desktop."


If you go

"Lost & Found: The Secrets of Archimedes" opens Sunday and runs through Jan. 1 at the Walters Art Museum, 600 N. Charles St. Tickets cost $6-$10. Call 410-547-9000 or go to thewalters.org.

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